v
Acknowledgments iii
Preface ix
Chapter 1 Introduction 1
Introductory Tutorial (Height Data) 4
A Linear Model for the Height Data 12
Cluster Analysis of the Height Data 15
FDA Flow Chart 21
Chapter 2 Basis Objects and Operations 23
What is a Basis? 24
Basis Objects 25
Choosing a Univariate Basis 26
Choosing a Bivariate Basis 28
Creating Univariate Bases 29
Creating Bivariate Bases 39
Operations on Univariate Bases 41
Operations on Bivariate Bases 44
Chapter 3 Functional Data Objects and Operations 45
Univariate Functional Data Objects (Pinch Force Example)48
Bivariate Functional Data Objects (Example) 61
Chapter 4 Linear Differential Operators and Smoothing
71
Linear Differential Operators 72
Smoothing via a Roughness Penalty 73
Specifying the Penalty Function 79
Chapter 5 Functional Registration 87
Analytic Registration 89
Lip Motion Example 91
Landmark Registration 96
Chapter 6 Functional Linear Models 101
Example with a Functional Dependent Variable 106
Example with Functional Independent Variables 110
Example with Functional Dependent and Independent
Variables 115
Chapter 7 Functional Generalized Linear Models 123
Weather Example 125
Polychotomous Classification 129
Chapter 8 Functional Principal Components 131
Analysis of the Bone Shape Data 135
Chapter 9 Canonical Correlation 145
Analysis of the Gait Data 147
Chapter 10 Functional Cluster Analysis 155
Clustering Precipitation Data 157
Clustering Temperature Data 162
Summary 164

Chapter 11 Principal Differential Analysis 165
S+FDA Functions for Principal Differential Analysis 168
Radioactive Decay Example 169
Harmonic Oscillator Example 173
Lip Movement Example 178
Appendix: References 187
Index 189